Derivative-Free Data-Driven Control of Continuous-Time Linear Time-Invariant Systems

TL;DR

This paper introduces a derivative-free, data-driven control method for continuous-time LTI systems using LMIs, which stabilizes systems based solely on input and output measurements without signal differentiation.

Contribution

It presents a novel LMI-based framework for stabilizing continuous-time LTI systems without derivatives, applicable to state-feedback and output-feedback scenarios.

Findings

Successfully stabilizes systems using only input/output data.

Employs low-pass filters to reconstruct plant signals without derivatives.

Validated through numerical examples demonstrating effectiveness.

Abstract

This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.